3/5n=1n

Solution for 3/5n=1n equation:

3/5n=1n

We move all terms to the left:

3/5n-(1n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+3/5n=0

We multiply all the terms by the denominator


-1n*5n+3=0

Wy multiply elements

-5n^2+3=0

a = -5; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-5)·3
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-5}=\frac{0-2\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-10}
=-\frac{\sqrt{15}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-5}=\frac{0+2\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-10}
=\frac{\sqrt{15}}{-5}
$